Geometrical models of interface evolution

Richard C. Brower, David A. Kessler, Joel Koplik, Herbert Levine

Research output: Contribution to journalArticlepeer-review

233 Scopus citations


We introduce a class of models for the motion of a boundary between time-dependent phase domains in which the interface itself satisfies an equation of motion. The intended application is to systems for which competing stabilizing and destabilizing forces act on the phase boundary to produce irregular or patterned structures, such as those which occur in solidification. We discuss the kinematics of moving interfaces in two or more dimensions in terms of their intrinsic geometric properties. We formulate local equations of motion as tractable simplifications of the complex nonlocal dynamics that govern moving-interface problems. Special solutions for dendritic crystal growth and their stability are analyzed in some detail.

Original languageEnglish
Pages (from-to)1335-1342
Number of pages8
JournalPhysical Review A
Issue number3
StatePublished - 1984
Externally publishedYes


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